[woodpusher]

There was a short period when two states were not part of the government currently operating at the time, but they were still apart of the United States of America."

States were never part of the Federal government, and are not part of the government today. The States are the members of the Union that created the Government.

Which branch of the government do find the States to be in? Legislative, Judicial, or Executive?

[BroJoeK]

woodpusher to OIFVeteran: "States were never part of the Federal government, and are not part of the government today.
The States are the members of the Union that created the Government."

Your first sentence is a minor quibble over words.
Your second sentence confirms OIFVeteran's point.

The Union exists since 1776 regardless of which specific forms its government takes.
States like North Carolina, Rhode Island and Vermont were never formally recognized as separated from that Union.